Effect of an Electric Field on the Structure and Stability of Atmospheric Clusters

We study the influence of an applied electric field on the structure and stability of some common bimolecular clusters that are found in the atmosphere. These clusters play an important role in new particle formation (NPF). For low values of the electric field (i.e., |E| ≤ 0.01 V Å–1), we demonstrate that the field response of the clusters can be predicted from simply calculating the dipole moment of the cluster and the dipole moments of the constituent molecules and that the influence on the association energy of the cluster is minimal (i.e., <0.5 kcal mol–1). For higher field strengths |E| > 0.2 V Å–1, there can be more dramatic effects on both structure and energetics, as the induced dipole, charge transfer, and geometric distortion play a larger role. Although such large fields are not very relevant in the atmosphere, they do exist in some situations of experimental interest, such as near interfaces and in intense laser fields.


Comparison of Two Methods for Applying an Electric
with electric field applied directly, or NWCHEM S2 with electric field approximated by point charges placed ±30 Å from the center of the oxygen atom.The NWCHEM optimizations were constrained to fix the position of the oxygen atom.

Effect of Including a Polarization Term
In Equation 9 of the main text, we model the field response of our systems simply as a linear response to the permanent, zero-field dipole moment µ.We can include an induced dipole by adding the polarizability α and modelling the field response as (1) The polarizability α is a tensor, but for our purposes we will simply assume it is isotropic so that we can express α as a single scalar quantity.
We computed polarizabilities with ORCA and in Figure S2 we show a version of Figure 1 from the main text, but including new results using the model of Equation S1 above.Quantitatively, inclusion of polarizability does improve agreement between our direct measurements and the dipole model.However, it is not very systematic.Inclusion of polarizability leads to an overestimate of the field response in most of the single molecules.In the bimolecular clusters, Equation S1 still under-estimates the field response, which we can attribute to the significant impact of field-driven molecular deformation on the cluster geometries, which is not included in models based on zero-field measurements.A similar exercise starting from Equation 10 in the main text gives us a way to include polarizability in an expression for the field dependence of the binding energy: Here ∆α = α clust − n 1 α i is defined the same way as ∆µ in the main text.Results from using Equation S2 instead of Equation 10 are shown in Figure S3.In all of the cases we studied, it turns out that ∆α is quite small, owing to near-cancellation of the polarizabilites of the cluster and the constituent molecules, so that there is almost no effect from including the polarizability in Equation S2.

Table of Optimized Energies for Single Molecules
Table S1: Electronic energies U field − U 0 , dipole moment µ, entropy term T S, and Gibbs free energies G field −G 0 for single molecules as a function of the electric field strength |E|, referred to results in zero field.All optimizations were done with the ωB97X functional S3-S5 including Grimme's D3 dispersion correction, S6,S7 and the cc-pVTZ basis set.Table S2: Electronic energies U field − U 0 , dipole moment µ, entropy term T S, and Gibbs free energies G field − G 0 for single molecules as a function of the electric field strength |E|.All calculation details are identical with Table S1 except for using the aug-cc-pVTZ basis set.Table S3: Electronic energies U field −U 0 , dipole moment µ, entropy term T S, Gibbs free energies G field − G 0 , and electronic association energies ∆U assoc and Gibbs free energy for association ∆G assoc as a function of the electric field strength |E| for clusters.All calculation details are identical with Table S2.Results in parentheses include BSSE.
Figure S1: Comparison of the field response of one H 2 O molecule, optimized using either ORCA S1 with electric field applied directly, or NWCHEM S2 with electric field approximated by point charges placed ±30 Å from the center of the oxygen atom.The NWCHEM optimizations were constrained to fix the position of the oxygen atom.

Figure S2 :
Figure S2: Figure1in the main text, but with added results using Equation S1 including the isotropic polarizability (dash-dotted lines).

Figure S3 :
Figure S3: Similar to Figure 3 in the main text, but using Equation S2 including the change in isotropic polarizability ∆α (dashed lines) to model the change in binding energy with field strength.

Table S4 :
CPU hours for a single numerical frequency calculation for different systems using different basis sets.All calculations used the ωB97X functional with the Grimme D3 dispersion correction, and were run with ORCA on one node of the Mahti supercomputer at Finland's CSC.

Table S5 :
Results of calculations with the ωB97X functional and the cc-pVTZ basis set, and Grimme's empirical D2 dispersion correction,S8for water, sulfuric acid, and the H 2 SO 4 •H 2 O cluster.